How the nuclear binding energy gives mass to the nucleus?

[HakimPhilo]

Hello everybody!
I have some difficulties concerning the concept of nuclear binding energy.
First, look at this example:
http://www.freeimagehosting.net/newuploads/jtefo.png
In the first case, the two protons have big energy. But this energy is not changing it's weight. And in the second case, when they collided, the energy that they contained transformed to new particles, so more mass.
But in the nuclear binding energy, when this energy converts into mass?

Thank you in advance...∞ :happy:

 

[Astronuc]

The example seems to be one of particle production rather than nuclear binding energy.

On the left side, the initial (rest?) mass is 0.3 unit, and on the right side one has 9 tracks, which are ostensibly particles and the total rest mass is now 1 unit. So the unknown or unspecified kinetic energy has been transformed into rest mass. It's not clear if the new particles are stable however.

 

[HakimPhilo]

Yes, but my question is when the energy of the proton converts to mass an how? We are speaking about the nuclear-binding energy.

 

[mfb]

For high-energetic particle collisions, nuclear binding energy is not relevant. You convert the kinetic energy of particles to mass of new particles.

"How": quantum field theory. It just happens, and theories can calculate the probabilities. There is no fundamental "reason" or "process" why/how it happens.

 

[HakimPhilo]

For high-energetic particle collisions, nuclear binding energy is not relevant. You convert the kinetic energy of particles to mass of new particles.

"How": quantum field theory. It just happens, and theories can calculate the probabilities. There is no fundamental "reason" or "process" why/how it happens.

We know that it happens but then the theory is incomplete since it can't explain how it happens.

 

[mfb]

The theory is not incomplete.
It is physics, not philosophy.
The theory can give you a model "how" it happens, it does not care if it is "real" (whatever that means).

 

[Bill_K]

We know that it happens but then the theory is incomplete since it can't explain how it happens.

Every theory has axioms. Plane geometry says that two lines meet in a point, but it's meaningless to pose the question "how" they do. That fact does not make plane geometry incomplete.

In this case we have an initial state A and a final state B, both with the same energy but with different particles having different masses. There is a term in the Hamiltonian that connects state A with state B, and therefore Schrodinger's Equation tells us there's a probability per unit time that A will evolve into B.

You may consider this to be mathematical and unintuitive, but mathematics is necessary for an understanding of quantum mechanics.